Hydrogen production is a common suggestion. Is it better?
Using the excess energy to produce hydrogen will depress the value of hydrogen until it's no longer profitable to produce hydrogen at those rates and then you have room for ball milling in the economics again.
Or until there's not enough excess energy to continue producing hydrogen; I don't see a reason why we'd expect the hydrogen to become unprofitable (water to become too expensive?) first.
Oil price changes disrupt oil operations all the time. The hydrogen energy economy will have times where it's not profitable for an individual actor to generate hydrogen too.
Aluminium production, hydrogen production, data centres, battery storage, sending it to other countries, etc.
You can't object "but then you have to build X" because you have to build stupid ball mills too. They aren't free.